The national curriculum for mathematics intends to ensure that all pupils:

1. become fluent in the fundamentals of mathematics, including through varied and frequent practice with increasingly complex problems over time, so that pupils develop conceptual understanding and the ability to recall and apply knowledge rapidly and accurately .

2. reason mathematically by following a line of enquiry, conjecturing relationships and generalisations, and developing an argument, justification or proof using mathematical language.

3. can solve problems by applying their mathematics to a variety of routine and non-routine problems with increasing sophistication, including breaking down problems into a series of simpler steps and persevering in seeking solutions.

The Maths Curriculum is delivered using the National Curriculum guidance 2014, and the Foundation Stage is followed to ensure continuity and progression.

The Intent, Implementation and Impact of our Mathematics Curriculum 

Historically, mathematics has been taught by memorising key facts and procedures, which tends to lead to a superficial understanding that can easily be forgotten. At Hallgate, we believe that children should be given the opportunity to gain a deeper understanding of mathematical concepts, enabling them to become autonomous in their learning and use and apply mathematical concepts across a broad and varied range of situations.

It is our belief that every child can achieve in mathematics and we want to eradicate a commonly held misconception that some pupils can 'do' maths and others cannot. A typical Maths lesson will provide the opportunity for all children, regardless of their ability or age, to work through Fluency, Reasoning and Problem Solving activities.

Intent

Maths is a journey from which many start at different places. At Hallgate, our intention is that children foster a love of mathematical learning, whatever their ability or starting place. We aim to provide children with a broad mathematical knowledge and understanding of the key mathematical concepts that they are able to confidently use and apply mathematical concepts across a variety of situations. We expect children to clearly articulate their ideas and thoughts and reasoning processes, enabling deeper learning. We expect children to make mistakes, analyse them and learn from them, justifying and explaining as they do this. At each stage of learning, children should be able to demonstrate a deep, conceptual understanding of the topic and be able to build on this over time.

There are 3 levels of learning:

• Shallow learning: surface, temporary, often lost
• Deep learning: it sticks, can be recalled and used
• Deepest learning: can be transferred and applied across a variety of different contexts

The deep and deepest levels are what we are aiming for by teaching maths using the Mastery approach. 

We aim to provide all children with some direct teaching every day, which is oral, interactive and stimulating. Teaching styles and lesson structure provide opportunities for children to consolidate their previous learning, use and apply their knowledge, understanding and skills, pose and ask questions, investigate mathematical ideas, reflect on their own learning and make links with other work.

Implementation

Multiple representations for all! 

Concrete, pictorial, abstract

Objects, pictures, words, numbers and symbols are everywhere. The mastery approach incorporates all of these to help children explore and demonstrate mathematical ideas, enrich their learning experience and deepen understanding. Together, these elements help cement knowledge so children truly understand what they’ve learnt and can apply them to other, unfamiliar mathematical situations.

We believe children learn best by moving from concrete first-hand experience, through pictorial/diagrammatic representation to secure abstract knowledge and understanding. When introduced to a key new concept, all children should have the opportunity to build competency in this topic by taking this approach and should be encouraged to move between the various stages as and when they need to. Children are encouraged to physically represent mathematical concepts and problems, explaining their reasoning as they do this. Objects and pictures are used to demonstrate and visualise abstract ideas, alongside numbers, language and symbols.

Concrete – children have the opportunity to use concrete objects and manipulatives to help them understand and explain what they are doing.

Pictorial – children then build on this concrete approach by using pictorial representations, which can then be used to reason and solve problems.

Abstract – With the foundations firmly laid, children can move to an abstract approach using numbers and key concepts with confidence.

Learning

In order to meet our aims, we believe that children must have exposure to a broad maths curriculum covering the 8 key areas set out by the National Curriculum:

• Place Value 
• Number ( + - x  ÷)
• Fractions 
• Measures
• Geometry  
• Statistics 
• Algebra (Year 6 Only) 
• Ratio and Proportion (Year 6 Only) 

Whilst learning the fluency of number is essential, we believe that the learning must provide lots of opportunities for children to explain their mathematical thinking and reasoning through: an encouragement to use practical resources, to create diagrams, to talk through thinking and to show their working out. Opportunities for application and problem solving are also essential to the children’s learning. 

All lessons should start with a thought-provoking question that will create opportunities for children to reason, discuss, explain and make connections between their mathematical understanding. The question must be related to the learning objective and/or based on a potential misconception presented by the objective. 

For example:

What’s the same? What’s different? 5 x 7 = 35, 50 x 7=350 

True or False?  48 + 48= 816

Always, Sometimes, Never? When two straight lines cross, there will be 4 right angles made.

Spot the error: 147 + 147 = 2814

Convince me: 3 x 4 = 4 x 3 

The rationale for the starter question is twofold; firstly, it is an early opportunity for AfL and secondly, it promotes mathematical discussion between children of differing ability levels. The question should be the basis for the lesson’s learning. Following this, there must be opportunities for paired or group learning before the children work independently in books. 

Paired and group learning should be centred around Active Learning Structures (e.g.Expert and Scribe/Fan and Pick) and, where necessary, involve practical activities, using resources, which again promote mathematical discussion, with the more able children generally supporting those less confident. 

A mathematical concept or skill has been mastered when a child can show it in multiple ways, using the mathematical language to explain their ideas, and can independently apply the concept to new problems in unfamiliar situations.

Assessment Informing Planning

Assessment activities are planned which involve a range of ideas and skills linked to one or more of the key objectives covered previously. A pre-assessment quiz at the start of each topic or block, ensures that teachers are able to accurately pinpoint gaps in children's knowledge and understanding and are able to plan lessons which address these gaps. At the end of each unit, the children are re-assessed focussing on the concepts they have covered and this informs future planning and teacher assessment throughout the year. 

Long-term assessments are undertaken through a combination of teacher assessment and end of term/ end of year summative assessment tasks. These are then used to inform parents of their child's progress and are passed onto the next teacher to inform future planning. 

Continuity and progression

The yearly teaching objectives and the termly planning sheets from the White Rose Framework are used consistently by all teachers to ensure continuity and progression across the school. Teachers also use the supplement of examples in the Framework to ensure that planned activities, irrespective of age and ability, are pitched at the right level.

Impact

Impact is evident in pupil voice; it shows that children enjoy maths lessons and relish a challenge. They feel that they are fully supported and know what to do when they need extra help. The children demonstrate a quick recall of facts and procedures and show confidence, believing that they will achieve. Books show  that the children have a high level of pride in the presentation and understanding of the work. Children have the flexibility and fluidity to move between different contexts and representations of mathematics.